Recent questions tagged determinant / GATE Overflow for GATE CSE

2 votes

2 answers

1

Memory Based GATE DA 2024 | Question: 4
Consider the matrix \[ \mathrm{M} = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6 \end{bmatrix} \] Find the value of $|\mathrm{M}^2 + 12M|$.

Consider the matrix\[\mathrm{M} = \begin{bmatrix}1 & 2 & 3 \\3 & 1 & 3 \\4 & 3 & 6\end{bmatrix}\]Find the value of $|\mathrm{M}^2 + 12M|$.

GO Classes

535 views

GO Classes asked Feb 4

32 votes

2 answers

2

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 7
Let $\mathrm{A}$ be a $3 \times 3$ matrix. Let $\mathbf{x}, \mathbf{y}, \mathbf{z}$ are linearly independent $3$ ... $\mathrm{A}$.

Let $\mathrm{A}$ be a $3 \times 3$ matrix. Let $\mathbf{x}, \mathbf{y}, \mathbf{z}$ are linearly independent $3$-dimensional vectors. Suppose that we have$$A \mathbf{x}=\...

GO Classes

1.4k views

GO Classes asked Mar 29, 2023

26 votes

4 answers

3

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 12
If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a $3 \times 3$ matrix $\mathrm{A},$ and $\operatorname{det(A)}=4,$ then $\alpha$ equals to?

If $P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$ is the adjoint of a $3 \times 3$ matrix $\mathrm{A},$ and $\operatorname{det(A)}...

GO Classes

1.2k views

GO Classes asked Mar 29, 2023

16 votes

2 answers

4

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 13
Given the following matrix: $ A=\left[\begin{array}{lll} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{array}\right] $ Consider the following statements: $A^2-4 A-5 I=0$ (where $I$ is ... following options is correct? Only $I$ is true. Only II is true. Both I and II are true. Neither I, nor II are true.

Given the following matrix:$$A=\left[\begin{array}{lll}1 & 2 & 2 \\2 & 1 & 2 \\2 & 2 & 1\end{array}\right]$$Consider the following statements:$A^2-4 A-5 I=0$ (where $I$ i...

GO Classes

974 views

GO Classes asked Mar 29, 2023

19 votes

5 answers

5

GO Classes CS/DA 2025 | Weekly Quiz 4 | Linear Algebra | Question: 15
Suppose $\mathbf{A}=\mathbf{B C}$, where $\mathbf{B}$ is a $4 \times 2$ matrix and $\mathbf{C}$ is a $2 \times 4$ matrix. Is $\mathbf{A}$ invertible? Yes, $\mathbf{A}$ is invertible. No, $\mathbf{A}$ is not invertible. Depends on $\mathbf{C}$ only. Depends on $\mathbf{B}$ and $\mathbf{C}$.

Suppose $\mathbf{A}=\mathbf{B C}$, where $\mathbf{B}$ is a $4 \times 2$ matrix and $\mathbf{C}$ is a $2 \times 4$ matrix. Is $\mathbf{A}$ invertible?Yes, $\mathbf{A}$ is ...

GO Classes

1.2k views

GO Classes asked Mar 29, 2023

21 votes

4 answers

6

GATE CSE 2023 | Question: 8
Let \[ A=\left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{array}\right] \] and \[ B=\left[\begin{array}{llll} 3 & 4 & ... $\operatorname{det}(B)=-\operatorname{det}(A)$ $\operatorname{det}(A)=0$ $\operatorname{det}(A B)=\operatorname{det}(A)+\operatorname{det}(B)$

Let\[A=\left[\begin{array}{llll}1 & 2 & 3 & 4 \\4 & 1 & 2 & 3 \\3 & 4 & 1 & 2 \\2 & 3 & 4 & 1\end{array}\right]\]and\[B=\left[\begin{array}{llll}3 & 4 & 1 & 2 \\4 & 1 & 2...

admin

11.3k views

admin asked Feb 15, 2023

4 votes

2 answers

7

GATE CSE 2023 | Memory Based Question: 13
Let $ A=\left[\begin{array}{llll} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{array}\right] $ ... $\operatorname{det} \mathrm{B}=-\operatorname{det} \mathrm{A}$ $\operatorname{det} \mathrm{A}=\operatorname{det} \mathrm{B}$

Let$$A=\left[\begin{array}{llll}1 & 2 & 3 & 4 \\4 & 1 & 2 & 3 \\3 & 4 & 1 & 2 \\2 & 3 & 4 & 1\end{array}\right]$$And$$B=\left[\begin{array}{llll}3 & 4 & 1 & 2 \\4 & 1 & 2...

GO Classes

2.5k views

GO Classes asked Feb 5, 2023

1 votes

0 answers

8

Self doubt.
If A, B & C are matrices & AB=AC then B=C? as we know it is not always true because when A is singular matrix then B=C not possible so what is the right ans to say B=C is (always not equal) or (may or may not be equal) or (simply not equal)?

If A, B & C are matrices & AB=AC then B=C?as we know it is not always true because when A is singular matrix then B=C not possible so what is the right ans to say B=C is ...

Nisha Bharti

497 views

Nisha Bharti asked Sep 19, 2022

1 votes

1 answer

9

TIFR CSE 2022 | Part A | Question: 4
Consider the polynomial $p(x)=x^3-x^2+x-1$. How many symmetric matrices with integer entries are there whose characteristic polynomial is $p$? (Recall that the characteristic polynomial of a square matrix $A$ in the variable $x$ is defined to be the determinant of the matrix $(A-x I)$ where $I$ is the identity matrix.) $0$ $1$ $2$ $4$ Infinitely many

Consider the polynomial $p(x)=x^3-x^2+x-1$. How many symmetric matrices with integer entries are there whose characteristic polynomial is $p$? (Recall that the characteri...

admin

709 views

admin asked Sep 1, 2022

0 votes

0 answers

10

Best Open Video Playlist for Determinants Topic | Linear Algebra
Please list out the best free available video playlist for Determinants Topic from Linear Algebra as an answer here (only one playlist per answer). We'll then select the best playlist and add to GO classroom video lists. ... standard ones are more likely to be selected as best. For the full list of selected videos please see here

Please list out the best free available video playlist for Determinants Topic from Linear Algebra as an answer here (only one playlist per answer). We'll then select the ...

makhdoom ghaya

232 views

makhdoom ghaya asked Aug 14, 2022

2 votes

1 answer

11

GO Classes Test Series 2023 | Linear Algebra | Test | Question: 9
Compute the determinant of $ A=\left[\begin{array}{cccc} 1 & -1 & 0 & 3\\ 2 & 5 & 2 & 6\\ 0 & 1 & 0 & 0\\ 1 & 4 & 2 & 1 \end{array}\right]. $

Compute the determinant of$$A=\left[\begin{array}{cccc}1 & -1 & 0 & 3\\2 & 5 & 2 & 6\\0 & 1 & 0 & 0\\1 & 4 & 2 & 1\end{array}\right].$$

GO Classes

381 views

GO Classes asked Aug 14, 2022

2 votes

1 answer

12

Applied Grand Test 2
What is the value of the given determinant ?

What is the value of the given determinant ?

LRU

764 views

LRU asked Nov 22, 2021

3 votes

1 answer

13

Applied Test Series
What is the value of the determinant ?

What is the value of the determinant ?

LRU

630 views

LRU asked Nov 13, 2021

8 votes

1 answer

14

GATE Overflow Test Series | Mock GATE | Test 2 | Question: 14
The value of determinant of non identity idempotent matrix is ________

The value of determinant of non identity idempotent matrix is ________

gatecse

554 views

gatecse asked Jan 17, 2021

1 votes

1 answer

15

GATE Overflow Test Series | Mixed Subjects | Test 4 | Question: 6
If $A = \begin{bmatrix}-12 & 7\\ -5 & 3 \end{bmatrix},$ then the value of $\text{det}(A^{2021})$ is _________

If $A = \begin{bmatrix}-12 & 7\\ -5 & 3 \end{bmatrix},$ then the value of $\text{det}(A^{2021})$ is _________

gatecse

103 views

gatecse asked Nov 27, 2020

1 votes

1 answer

16

GATE Overflow Test Series | Mixed Subjects | Test 4 | Question: 7
If det $\begin{pmatrix} 2 &\alpha\\ 3 & \beta \end{pmatrix} = 16$ and det $\begin{pmatrix} 2 &\beta\\ 3 & \alpha \end{pmatrix} = 1,$ then the value of $\alpha^{2} + \beta^{2}$ is _________

If det $\begin{pmatrix}2 &\alpha\\3 & \beta\end{pmatrix} = 16$ and det $\begin{pmatrix}2 &\beta\\3 & \alpha\end{pmatrix} = 1,$ then the value of $\alpha^{2} + \beta^{2}$ ...

gatecse

75 views

gatecse asked Nov 27, 2020

2 votes

1 answer

17

GATE Overflow Test Series | Mixed Subjects | Test 4 | Question: 19
If $\alpha,\beta$, and $\gamma$ are the roots of the equation $x^{3} + 3x^{2} - 2x + 4 = 0$ then the value of the determinant $\begin{vmatrix} \alpha & \beta & \gamma\\ \beta & \gamma & \alpha\\ \gamma & \alpha & \beta\\ \end{vmatrix}$ is __________

If $\alpha,\beta$, and $\gamma$ are the roots of the equation $x^{3} + 3x^{2} - 2x + 4 = 0$ then the value of the determinant $\begin{vmatrix}\alpha & \beta & \gamma\\\be...

gatecse

163 views

gatecse asked Nov 27, 2020

3 votes

1 answer

18

GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 3
The value of the determinant $\begin{vmatrix} 2\alpha & \alpha + \beta & \alpha + \gamma\\ \beta + \alpha & 2\beta & \beta + \gamma\\ \gamma + \alpha & \gamma + \beta & 2\gamma \end{vmatrix}$ is ________

The value of the determinant $\begin{vmatrix}2\alpha & \alpha + \beta & \alpha + \gamma\\\beta + \alpha & 2\beta & \beta + \gamma\\\gamma + \alpha & \gamma + \beta & 2\ga...

gatecse

257 views

gatecse asked Oct 30, 2020

1 votes

1 answer

19

GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 6
Which of the following is/are correct? (Mark all the appropriate choices) The value of a determinant remains unaltered, if the rows and columns are interchanged. If two rows (or two columns) of a determinant are interchanged, the ... or column) of a matrix are multiplied by a constant $k,$ the determinant also gets multiplied by $k.$

Which of the following is/are correct? (Mark all the appropriate choices)The value of a determinant remains unaltered, if the rows and columns are interchanged.If two row...

gatecse

238 views

gatecse asked Oct 30, 2020

2 votes

1 answer

20

GATE Overflow Test Series | Linear Algebra | Test 1 | Question: 10
Which of the following is/are correct? (Mark all the appropriate choices) The determinant of a skew-symmetric matrix over real numbers is non-negative. When the identity matrix is added to a real skew-symmetric matrix, the resultant matrix is invertible. ... a zero matrix. For two matrices $A$ and $B,$ if $AB = 0,$ then $BA = 0.$

Which of the following is/are correct? (Mark all the appropriate choices)The determinant of a skew-symmetric matrix over real numbers is non-negative.When the identity ma...

gatecse

331 views

gatecse asked Oct 30, 2020

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